Question 1097081
<pre>
Let "a", "b" and "c" be the rate-of-work of each of the persons A, B, and C respectively.

We are given that 

a + b = {{{1/4}}},      (1)
b + c = {{{1/3}}},      (2)
a + c = {{{1/2.4}}}.    (3)

To solve the system (1), (2), (3), let us start adding the equations (1), (2) and (3).
You will get 

2a + 2b + 2c = {{{1/4 + 1/3 + 1/2.4}}} = {{{6/24 + 8/24 + 10/24}}} = {{{(6+8+10)/24}}} = 1.

Hence, 

a + b + c = 1/2.    (4)

Thus we just found the combined rate-of-work of the three persons working together. It is {{{1/2}}} of job per day.


Now we have to find individual rate-of-work for each person. For it, let us first subtract the equation (1) from (4). You will get

c = {{{1/2 - 1/4}}} = {{{1/4}}}.


Next, subtract the equation (2) from (4). You will get

a = {{{1/2 - 1/3}}} = {{{1/6}}}.


Finally, subract the equation (3) from (4). You will get

b = {{{1/2 - 1/2.4}}} = {{{12/24 - 10/24}}} = {{{2/24}}} = {{{1/12}}}.


<U>Answer</U>. The individual rates of work are {{{1/4}}} for C, {{{1/6}}} for A and {{{1/12}}} for B (in job-per-day units).

        So,  A will complete the job in 6 days;  B will complete the job in 12 days;  and C will complete the job in 4 days.
</pre>


For many other similar solved problems See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Joint-work-word-problems-for-3-4-5-participants.lesson>Joint-work problems for 3 participants</A>

in this site.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this textbook under the topic 
"<U>Rate of work and joint work problems</U>" &nbsp;of the section &nbsp;"<U>Word problems</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.



================
<U>Notice</U>.  &nbsp;The way on how I solved the system of equations is &nbsp;<U>THE &nbsp;STANDARD &nbsp;WAY</U>&nbsp; of dealing with such special systems.



The way that @gosgarithmetic proposes in his solution is the way to &nbsp;NOWHERE.